The problem describes a debt to be amortized. $($Round your answers to the nearest cent.$)$A man buys a house for $$\backslash$$ $360,000$$$.$ He makes a $$\backslash$$ $150,000$$ down payment and amortizes the rest of the purchase price with semiannual payments over the next $14$ years. The interest rate on the debt is $$12\backslash \%$$$,$ compounded semiannually.$($a$)$ Find the size of each payment.s$($b$)$ Find the total amount paid for the purchase.$\backslash$$$($c$\backslash )$ Find the total interest paid over the life of the loan.$s$